The Lagrangian for mass dimension one fermionic dark matter

Abstract

The mass dimension one fermionic field associated with Elko satisfies the Klein-Gordon but not the Dirac equation. However, its propagator is not a Green's function of the Klein-Gordon operator. We determine the operator in which the associated Green's function is the propagator of the fermionic field. The field is still of mass dimension one, but the obtained Lagrangian resolves the last outstanding issue of mass dimension one fields. This Lagrangian does not admit local gauge invariance. Therefore, the mass dimension one fermions have limited interactions with the Standard Model particles and are natural dark matter candidates.